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Year 5 Maths Angles

Measure angles with a protractor

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Theory

Angles are measured in degrees (\(^\circ\)) with a protractor. Put the centre on the vertex, line the base line up with one arm, then read the scale that starts at \(0\) on that arm. This Year 5 maths page shows how to place the protractor, how to pick the right one of its two scales, and how to catch a wrong-scale reading by estimating first.

An angle is the amount of turn between two arms that meet at a point called the vertex. It is measured in degrees: a right angle is \(90^\circ\) and a straight angle is \(180^\circ\).

A protractor has a centre mark on its straight edge and two scales from \(0^\circ\) to \(180^\circ\) running in opposite directions.

To measure, put the centre mark exactly on the vertex and the base line along one arm. Use the scale that reads \(0\) on that arm and count up to where the other arm crosses.

At any mark the two scales add to \(180^\circ\) (for example \(50\) and \(130\)). If you read the wrong scale, the correct size is \(180^\circ\) minus your reading.

Protractor measuring a 50 degree angle A protractor with its centre on the vertex. One arm lies along the base line to the right, where the inner orange scale reads 0. The other arm crosses the inner scale at 50 and the outer scale at 130. The angle is 50 degrees. 180160140120100806040200 020406080100120140160180 centre on the vertex
The arm along the base points right, where the inner scale reads \(0\). Read the inner scale: \(50^\circ\).
Protractor measuring a 145 degree angle from the left A protractor with its centre on the vertex. One arm lies along the base line to the left, where the outer blue scale reads 0. The other arm crosses the outer scale at 145 and the inner scale at 35. The angle is 145 degrees. 180160140120100806040200 020406080100120140160180 centre on the vertex
Here the base arm points left, where the outer scale reads \(0\). Read the outer scale: \(145^\circ\).

Protractor facts:

\[ \text{inner reading} + \text{outer reading} = 180^\circ \]
inner reading + outer reading =180
\[ \text{correct size} = 180^\circ - \text{wrong-scale reading} \]
correct size =180− wrong-scale reading
Estimate first. If the angle is smaller than a right angle, the answer must be less than \(90^\circ\). That tells you which of the two numbers is right.
Start from zero. Follow the scale that has \(0\) on the arm along the base line.

How to measure an angle

  1. Estimate: is it less than or more than a right angle?
  2. Place the centre mark on the vertex.
  3. Line up the base line with one arm.
  4. Choose the scale that reads \(0\) on that arm.
  5. Read where the other arm crosses that scale, and check it matches your estimate.
Example 1 — Inner scale
Use the first diagram. What is the size of the angle?
Solution
\(\text{inner scale}\)\(=\)\(50^\circ\)
50

\(50^\circ\). It is less than a right angle, so \(130\) cannot be right.

Example 2 — Outer scale
Use the second diagram. What is the size of the angle?
Solution
\(\text{outer scale}\)\(=\)\(145^\circ\)
145

\(145^\circ\), an angle more than a right angle.

Example 3 — Both scales
An angle is measured from an arm pointing right. The second arm crosses the inner scale at \(125\).
(i) What does the outer scale read there?
(ii) What is the size of the angle?
Solution
\(180 - 125\)\(=\)\(55\)
180−125=55

(i) \(55\)
(ii) \(125^\circ\), from the scale that starts at \(0\) on the arm.

Example 4 — Wrong-scale readings
Each reading was taken on the wrong scale. Find the correct size.
(i) \(165^\circ\)
(ii) \(85^\circ\)
Solution
\(180 - 165\)\(=\)\(15^\circ\)
\(180 - 85\)\(=\)\(95^\circ\)
180−165=15,180−85=95

(i) \(15^\circ\)
(ii) \(95^\circ\)

Example 5 — Placing the protractor
Which placement is correct? (A) centre mark on the vertex, base line along one arm; (B) the end of the straight edge on the vertex; (C) centre mark on one arm.
Solution

A. Only the centre mark on the vertex, with the base line along an arm, gives a true reading.

Example 6 — Check with an estimate
An angle is clearly bigger than a right angle. Jun measures it as \(35^\circ\). What has happened, and what is the real size?
Solution
\(180 - 35\)\(=\)\(145^\circ\)
180−35=145

He read the wrong scale. The angle is \(145^\circ\).

Example 7 — A right angle
Why do both scales read \(90\) for a right angle?
Solution
\(180 - 90\)\(=\)\(90\)
180−90=90

The two readings always add to \(180\), and half of \(180\) is \(90\), so both scales meet there.

Common pitfalls

Reading the wrong scale. Use the scale with \(0\) on the base arm. A wrong-scale reading is \(180^\circ\) minus the true size.
Lining up the edge of the protractor, not the centre mark. The centre mark must sit exactly on the vertex.
Arms too short to reach the scale. Extend the arms with a ruler first; this does not change the angle.
Skipping the estimate. An estimate shows at once whether the answer should be under or over 90 degrees.

Frequently asked questions

What unit are angles measured in?

Degrees, written with a small circle: \(50^\circ\).

Why does a protractor have two scales?

So you can measure from an arm pointing either left or right. Each scale starts at 0 on one side.

Which scale should I read?

The one that reads \(0\) on the arm lying along the base line.

How do I fix a wrong-scale reading?

Subtract it from \(180^\circ\). A reading of \(165^\circ\) on the wrong scale means the angle is \(15^\circ\).

Where does the protractor go?

Centre mark on the vertex, base line along one arm.

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